I wouldn't expect a window A/C unit in the rear window to cool the front part - there's nothing to drive the cool air all the way up front. This is why RV roof top A/C units are located more towards the middle. Maybe a fan would help move the cool air further forward?
RVs are not insulated all that well and a 1981 may not have much at all in the roof. With all of the sun beating down on the roof, one small window A/C isn't going to make it. Yes, he should install a roof unit and it should be a larger one if they want to be comfortable.
Bill